Control of an adaptive refinement technique of generalized cell mapping bysystem dynamics

Generalized cell mapping is an efficient and powerful numerical tool for th e prediction of the long-term behavior and global analysis of nonlinear dyn amic systems. The only drawback of this method is the enormous computationa l effort it requires for high-dimensional systems. We overcome this problem by adaptively refining a very rough starting cell grid, where the adaptati on is controlled by the long-term dynamics of the system. We illustrate the efficiency of our approach by examples.